## Work Done By The Human Heart

I was reading a book on thermodynamics and for some reason they threw in the fact that each beat of a human heart is about 1 joule. Of course I did what any self-respecting scientist does, I reached for the nearest envelope and started calculating things.

The heart is nothing more than a pump that forces a fluid through the pipes of the body by contracting its volume so I should be able to find the work done by the heart from the change in volume and blood pressure. At the time I was doing this I didn’t have a computer handy so I had to guess. It really is a good idea to make an educated guess before reaching for the internet (I thought I read somewhere that the internet is making us stupid, but I can’t remember where I saw that. Guess I’ll have to look that up later). Even though I was just at the the doctor I don’t remember what my blood pressure is, but I do know that 120/80 is a tad high. What are the units? Hmmm. I’m embarassed to admit I didn’t remember but I know 120 is a pretty large pressure in psi (your car tires are only around 40 psi) and I doubt the American medical community would use Pascals so 120 must by mm of Mercury (or mm Hg). Since blood pressure varies between 120 at a high and 80 at the low, I’ll choose 100 as the “average” simply because it’s easy to work with.  I know there are about 0.02 psi in 1 mm Hg so 100 mm Hg = 2.0 psi.  There are 4.4 N to the pound and 2.54 cm to the inch so 1 psi = 4.4 N / (2.54 cm)2 = 3 N/10 cm2 = .3 N/cm2.  Put this all together to get 100 mm Hg = 0.6 N/cm2.

The next thing needed is a volume of the human heart.  I’ve heard the heart is about the size of a fist so my fist looks to be about 10 cm by 3 cm by 3 cm (I know my numbers are off but I’m choosing easy numbers) which yields a volume of about 100 cm3. Lets put it all together.  The work done by a pump, operating at constant pressure is W = PΔV (the Greek letter Δ can be read as “change in…” so ΔV is the change in volume) so the work done by the human heart is roughly W = 0.6 N/cm2 × 100 cm3 = 60 N cm = 0.6 N m = 0.6 J.  This means that the initial value of 1 J per heart beat is physically reasonable.

Now I’m willing to bet that many intro physics students wouldn’t remember how to find the work done by a pump, but they can still figure out the work done by the heart.  The secret is to model the heart as a piston with the same volume as the heart.  Assume the piston head has an area of 10 cm2 and the cylinder is 10 cm long (this gives a volume of 100 cm3, which matches with my previous estimate, and makes the math really easy).  For a constant force, every intro student knows that the work done is equal to the force multiplied by the distance the force pushes, W=Fd.  Using my earlier value of 100 mm Hg = 0.6 N/cm2 , the 10cm2 piston must push with a force of F= PA = 0.6 N/cm2 × 10cm2 = 6.0 N.  Then the work done is just this force multiplied by how far the piston is pushed or W=6.0 N × 10 cm = 60 N cm = 0.6 N m or 0.6 J!

The book,  Introduction to Biological Physics for the Health Sciences, lists the work done by the heart per beat as 0.5 Joules.  I’m not sure were that number came from, but it does agree closely with my estimate.  Other sites on the web list a value of 0.5 J or 1 J, but I can’t find where these numbers are coming from.  At least my estimate agrees with what everyone else thinks is the correct value.

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### 8 Responses to Work Done By The Human Heart

1. Matt says:

Okay, so if the human heart does 0.6 J of work per beat and there are about 0.00024 kcal in a joule, that’s 1.44×10-4 kcal per beat. If you assume a low-end rate of 60 beats/second, that’s about 8.64×104 beats/day. Put ‘em together and you get about 12.4 kcals per day. that’s somewhere around 6-8% of your recommended daily (food) calorie intake. Funny – I’d have thought it would be more…

• al says:

60 beats/( min ), check ur denominator of low-end beat rate.

2. Matt says:

Hmmm, my exponents didn’t go into super-scripts…

3. Wikipedia claims the heart accounts for 7% of daily energy expenditures, 30% to the liver, 20% to the brain and another 20% to the skeletal muscles, and 10% to the kidneys, with the remainder going to other organs. I’m really surprised (and a little dubious) at how close my estimate is to what I’m finding on other sites. I haven’t found a source of information that I truly trust on this topic.

4. rszimmerma says:

Blood pressure is measured in mm of Hg.

5. Iustinianos says:

But what about efficiency of the heart ? It is nearly 20% and your estimation is only that portion. Multiply it by 5.

6. Alumuku says:

Good thinking.

7. JJ says:

Thanks for the thinking process! I am doing an Honors projects on studying human’s heart through the lenz of physics. I came to the point of figuring out how much work heart does at each beat. Most materials I found only gave the result but without the calculation process. Great explaination! Thanks!!!!